Poissonian asymptotics of a randomly perturbed dynamical system: Flip-flop of the stochastic disk dynamo
The authors consider random perturbations of the flow generated by the 2-dimensional vector field \((-\mu x_1+x_1x_2,-\nu x_2+1-x_1^2)\) which describes a single-disk dynamo model and has two stable and one saddle type fixed points. They show that when parameter of perturbations tends to zero the process counting the number of transitions between basins of attracting points with properly scaled time converges (in the sense of convergence of finite-dimensional distributions) to a Poisson process. This stochastic disk dynamo model was proposed previously by the first author [J. Stat. Phys. 53, 19-39 (1988)] as a model of reversals of Earth's magnetic field.
scientific article; zbMATH DE number 1279701
scientific article